Following the path of [1]}, we construct \(\sigma _h\)  patchwise around the mesh vertices using Arnold–Falk–Winther mixed finite element spaces [2]}, which are based on a stress tensor constructed in the Brezzi–Douglas–Marini space (see, e.g., [3]} and [4]}), along with Lagrange multipliers that enforce a weak symmetry constraint.
From this point on, \(\mathcal {V}_h^D\)  will denote the set collecting all mesh vertices which lie on some Dirichlet boundary face. Notice that \(\mathcal {V}_h^D\)  also contains the vertices lying at the intersection between \(\Gamma _D\)  and \(\Gamma _{\bullet }\) , \(\bullet \in \lbrace N, C\rbrace \) .
